In this subsection we list a few results used in our proofs. Some of them may be considered as special cases of the Pink-Zilber conjectures (see [1]} and [2]}) whereas the last one is taken from the theory of \(S\) -unit equations (see [3]}). We believe that this recall may be helpful for some readers; some of these theorems go back to some time ago, whereas others are more recent.
